The experimental program ¨SPC-PM Po 3D¨ is part of the ongoing research of the Chemnitz research group Scientific Parallel Computing (SPC) into finite element methods for problems over three dimensional domains. The package in its version 2.0 is documented in two manuals. The User's Manual provides an overview over the program, its capabilities, its installation, and handling. Moreover, test examples are explained. The aim of the Programmer's Manual is to provide a description of the algorithms and their realization. It is written for those who are interested in a deeper insight into the code, for example for improving and extending. In Version 2.0 the program can solve the Poisson equation and the Lam\'e system of linear elasticity with in general mixed boundary conditions of Dirichlet and Neumann type. The domain $\Omega\subset\R^3$ can be an arbitrarily bounded polyhedron. The input is a coarse mesh, a description of the data and some control parameters. The program distributes the elements of the coarse mesh to the processors, refines the elements, generates the system of equations using linear or quadratic shape functions, solves this system and offers graphical tools to display the solution. Further, the behavior of the algorithms can be monitored: arithmetic and communication time is measured, the discretization error is measured, different preconditioners can be compared. We plan to extend the program in the next future by including a multigrid solver, an error estimator and adaptive mesh refinement, as well as the treatment of coupled thermo-elastic problems. The program has been developed for MIMD computers; it has been tested on Parsytec machines (GCPowerPlus-128 with Motorola Power PC601 processors and GCel-192 on transputer basis) and on workstation clusters using PVM. The special case of only one processor is included, that means the package can be compiled for single processor machines without any change in the source files.

Using material models on the basis of the flow theory of plasticity the asymptotic behaviour of solid mechanics solutions in crack tips, interface corners etc. strongly depends on the local realized load trajectory. For incrementally proportional load paths the equations determining the asymptotic fields are very simple ones. The paper considers two-dimensional statements in the neighbourhood of an interface corner consisting of two material ranges. At a distance from the corner the finite element nodes of a regular net are established in a polar co-ordinate system together with the displacement degrees of freedom. The main idea of the presented singular and non-singular stress and deformation field calculation at interface corners characterizes an replacement of the corner neighbourhood effect to the surrounding body by introducing stiffness actions which in usual manner can be assembled together with the other element stiffness matrices to the global stiffness matrix of the body. According to this there exists an in teresting invariant stiffness independence in corner and crack neighbourhoods. The applied technique allows extensions to non-proportional local load increments simplifying the mathematical calculations for the presentation of stress and strain fields in this general case. All computations are made on modern parallel computers. Concrete examples show the advantages of the presented approach.

We report on calculations of smoothed spectral correlations in the twodimensional Anderson model for weak disorder. As pointed out in (M. Wilkinson, J. Phys. A: Math. Gen. 21, 1173 (1988)), an analysis of the smoothing dependence of the correlation functions provides a sensitive means of establishing consistency with random matrix theory. We use a semiclassical approach to describe these fluctuations and offer a detailed comparison between numerical and analytical calculations for an exhaustive set of two-point correlation functions. We consider parametric correlation functions with an external Aharonov-Bohm flux as a parameter and discuss two cases, namely broken time-reversal invariance and partial breaking of time-reversal invariance. Three types of correlation functions are considered: density-of-states, velocity and matrix element correlation functions. For the values of smoothing parameter close to the mean level spacing the semiclassical expressions and the numerical results agree quite well in the whole range of the magnetic flux.

In this paper we compare the performance, scalability, and robustness of different parallel algorithms for the numerical solution of nonlinear boundary value problems arising in the magnetic field computation and in solid mechanics. These problems are discretized by using the finite element method with triangular meshes and piecewise linear functions. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely multigrid methods and conjugate gradient methods with preconditioners based on domain decomposition, multigrid, or BPX techniques, respectively. The basis of the implementation of all solvers is a non-overlapping domain decomposition data structure such that they are well-suited for parallel machines with MIMD architecture.

We study two interacting particles in a random potential chain by means of the transfer matrix method. The dependence of the two-particle localization length lampta_2 on disorder and interaction strength is investigated. Our results demonstrate that the recently proposed enhancement of lampta_2 as compared to the results for single particles is entirely due to the finite size of the systems considered. This is shown for a Hubbard-like onsite interaction and also a long-range interaction.

Asynchronous iterations often converge under different conditions than their syn- chronous counterparts. In this paper we will study the global convergence of Jacobi- Newton-like methods for nonlinear equationsF x = 0. It is a known fact, that the synchronous algorithm converges monotonically, ifF is a convex M-function and the starting valuesx0 andy0 meet the conditionF x04 04F y0 . In the paper it will be shown, which modifications are necessary to guarantee a similar convergence behavior for an asynchronous computation.

We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder 1 c ss U= 2. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.

We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in the center of the band which show critical behavior up to the system size N=200x200 considered. This result is confirmed by an independent analysis of the localization lengths in quasi-1D strips with the help of the transfermatrix method. Adding a very small additional onsite potential disorder, the critical states become localized.

We study two interacting particles in a random potential chain by a transfer matrix method which allows a correct handling of the symmetry of the two- particle wave function, but introduces an artificial ¨bag¨ interaction. The dependence of the two-particle localization length lambta 2on disorder, interaction strength and range is investigated. Our results demonstrate that the recently proposed enhancement of lambta 2 as compared to the results for single particles is vanishingly small for a Hubbard interaction. For longer-range interactions, we observe a small enhancement but with a different disorder dependence than proposed previously.

Der Ersatz von geschädigtem Gewebe durch körpereigene Reparaturprozesse wird auf zellulärer Ebene durch Stammzellen unterstützt. Diese Regenerationsfähigkeit ist allerdings in einigen Geweben nur eingeschränkt vorhanden. So kommt es bei der Sehnenheilung des Pferdes unter konventioneller Therapie zur narbigen Reparation mit hohen Rezidivraten. Die Anwendung von multipotenten mesenchymalen Stromazellen (MSC) stellt eine innovative Therapiemethode dar, da die tenogene Differenzierung zum Zellersatz mit anschließender Matrixmodulation führen könnte. Es ist jedoch unklar, ob eine entzündliche Umgebung in diesem Zusammenhang Einfluss auf funktionelle Eigenschaften der MSC hat. In dieser Arbeit wurden erstmalig funktionelle Eigenschaften, mit dem Fokus des tenogenen Differenzierungspotentials, von aus Fettgewebe isolierten equinen MSC, unter dem Einfluss proinflammatorischer Zytokine und einer direkten Leukozyten-Ko-Kultur, untersucht. Es wurde ein komplexes In-vitro-Modell entwickelt, um die in vivo vorherrschenden Bedingungen bestmöglich zu berücksichtigen. Es konnte erstmals nachgewiesen werden, dass funktionelle und tenogene Eigenschaften von MSC in einem komplexen In-vitro-Modell unter dem Einfluss von proinflammatorischen Zytokinen oder Leukozyten beeinträchtigt werden. Dies hebt die Notwendigkeit zur Untersuchung der komplexen Zusammenhänge während einer akuten Entzündungsreaktion hervor. Es bleibt zu klären, ob trotz der starken Beeinflussung der tenogenen Eigenschaften der vorherrschende Mechanismus der Stammzell-unterstützten Sehnenheilung die tenogene Differenzierung der MSC sein kann.:Inhaltsverzeichnis 1 Einleitung 2 Literaturübersicht 2.1 Multipotente mesenchymale Stromazellen 2.1.1 Eigenschaften 2.1.2 Quellen und Charakterisierung 2.1.3 Therapeutisches Potential 2.2 Pathologie der equinen oberflächlichen Beugesehne 2.2.1 Tiermodell Pferd 2.2.2 Erkrankungen der equinen oberflächlichen Beugesehne 2.2.3 Die Bedeutung der Entzündungsreaktion 2.2.4 Die Bedeutung proinflammatorischer Zytokine und Leukozyten 2.3 Therapeutische Möglichkeiten zur Behandlung von Sehnenpathologien 2.4 Sehnen-Tissue Engineering 2.5 Induktion der tenogenen Differenzierung von MSC 2.6 Bioreaktorsysteme im Sehnen-Tissue Engineering 3 Zielstellung und Hypothesen 4 Tiere, Material und Methoden 4.1 Mesenchymale Stromazellen 4.1.1 Tiere 4.1.2 Material 4.1.3 Methoden 4.1.3.1 Auftauen von AT-MSC 4.1.3.2 Kultivierung von AT-MSC 4.1.3.3 Passagieren von AT-MSC 4.2 Equine oberflächliche Beugesehnen 4.2.1 Material 4.2.2 Methoden 4.2.2.1 Gewinnung von equinen OBS 4.2.2.2 Dezellularisierung von equinen OBS 4.2.2.3 Zuschnitt zu Sehnenscaffolds 4.3 Leukozyten 4.3.1 Spendertier 4.3.2 Material 4.3.3 Methoden 4.3.3.1 Blutentnahme 4.3.3.2 Leukozytenisolierung durch Dichtegradientenzentrifugation 4.3.3.3 Leukozytenstimulation 4.4 Versuchsaufbau 4.5 Aussaat von Scaffold- und Monolayerkulturen 4.5.1 Material 4.5.2 Methoden 4.5.2.1 Monolayerkulturen 4.5.2.2 Scaffoldkulturen 4.6 Bioreaktor 4.7 Stimulation und Stimulationsmuster 4.8 Zugabe von Zytokinen 4.9 Auswertung 4.10 Phasenkontrastmikroskopie und Zellzahlbestimmung 4.10.1 Material 4.10.2 Methoden 4.10.2.1 Automatisierte Auswerung von Aufnahmen der Phasenkontrastmikroskopie 4.10.2.2 Zellzahlbestimmung 4.11 Lebend/Tot-Färbung 4.11.1 Material 4.11.2 Methoden 4.11.2.1 Lebend/Tot-Färbung der Monolayerkulturen 4.11.2.2 Lebend/Tot-Färbung der Scaffoldkulturen 4.11.2.3 Auswertung 4.12 Histologie 4.12.1 Material 4.12.2 Methoden 4.12.2.1 Fixierung und Paraffineinbettung 4.12.2.2 Mikrotomschnitte 4.12.2.3 Hämatoxylin-Eosin-Färbung 4.12.2.4 Auswertung 4.13 Real-Time PCR 4.13.1 Material 4.13.2 Methoden 4.13.2.1 RNA-Isolierung aus Scaffoldkulturen 4.13.2.2 Zellaufschluss der Monolayerkulturen 4.13.2.3 cDNA-Synthese durch Reverse Transkription 4.13.2.4 Real-Time PCR 4.14 Tripotente Differenzierung 4.14.1 Material 4.14.2 Methoden 4.14.2.1 Zellaussaat, Kultivierung und Fixierung 4.14.2.2 Färbung der adipogenen Differenzierung 4.14.2.3 Färbung der osteogenen Differenzierung 4.14.2.4 Färbung der chondrogenen Differenzierung 4.14.2.5 Automatische Auswertung 4.15 Statistische Auswertung 5 Ergebnisse 5.1 Morphologie, Proliferation und Konfluenz der MSC 5.2 Lebend/Tot-Färbung 5.3 Hämatoxylin-Eosin-Färbung 5.4 Genexpression der muskuloskelettalen Marker 5.4.1 Monolayerkultur 5.4.2 Unstimulierte Scaffoldkultur 5.4.3 Stimulierte Scaffoldkultur 5.4.4 Vergleichende Analyse der Versuchsreihen 5.5 Tripotente Differenzierung 5.5.1 Adipogene Differenzierung 5.5.2 Chondrogene Differenzierung 5.5.3 Osteogene Differenzierung 6 Diskussion 6.1 Diskussion der verwendeten Methoden 6.2 Diskussion der Ergebnisse 6.3 Schlussfolgerung 7 Zusammenfassung 8 Summary 9 Literaturverzeichnis 10 Anhang 10.1 Herstellung von Reagenzien 10.2 RNA-Isolierung mittels RNeasy Mini Kit® 10.3 Färbeprotokolle 10.4 Herstellung von Silikonschalen 10.5 Extreme Ausreißerwerte der Genexpressionsanalysen 10.5.1 Monolayerkultur 10.5.2 Unstimulierte Scaffoldkultur 10.5.3 Stimulierte Scaffoldkultur Danksagung